The paper proves that algorithmic safety verification for Turing‑complete, self‑modifying systems—whether fixed or recursively self‑improving—is fundamentally limited. Statistically, no verifier can be sound, complete, and tractable across unbounded domains, all finite configurations, or succinctly described finite environments, due to Rice’s, Gödel’s, Trakhtenbrot’s, coNP, and PSPACE barriers. Dynamically, even a single self‑modification step can render safety properties undecidable, and no total supervisory algorithm can guarantee correctness for all such transformations, though a monitor that raises alarms on violations remains feasible.
whyItMatters":"The results show that formal safety guarantees for recursive self‑improvement are unattainable, highlighting intrinsic verification barriers for advanced AI systems."
By Jose Pascual Gumbau Mezquita
arXiv:2609.06036v1 Announce Type: new
Abstract: Proposal-based controllers---learned policies, language-model planners, and other black-box \emph{generators}---are increasingly deployed behind runtim...
By Guangxi Wan, Yongbo Xie, Yuqi Liu, Qingwei Dong, Qingxin Li, Hongfei Bai, Peng Zeng
arXiv:2609. 11326v2 Announce Type: replace-cross Abstract: We ask whether it can be certified algorithmically that a self-modifying computational system preserves a safety property at its next step (preservation) and along its whole evolution (persistence).
By Jose Pascual Gumbau Mezquita
arXiv:2607. 11951v1 Announce Type: new Abstract: Large language models can write SQL, but enterprise deployment demands more than plausible text: outputs must be syntactically valid, must respect per-role and per-schema policy, must carry provable (not best-effort) guarantees, must not slow down as generations grow, and must leave a compliance-grade record of every decision.
By Mohsen Arjmandi
The paper presents a production streaming guardrail system that ensures exact release‑boundary equivalence for language‑model outputs. It compiles regular‑language predicates into persistent NFAs, distinguishes stable from provisional states, and applies document‑order priority to decide before each chunk release. Evaluations on over 200,000 partitioned cases show zero mismatches and demonstrate that incremental matching can outperform native regex at larger chunk sizes while remaining competitive at smaller ones.
By Christopher M. Frost
arXiv:2607. 22868v1 Announce Type: new Abstract: Runtime guardrails act before irreversible tool calls, but their guarantees depend on what policy state is representable, what a judge observes, and whether intervention changes future behavior.
By Shawn Ray